1. Field of the Invention
The present invention relates generally to systems using adaptive digital filters, and more specifically, to an adaptive digital filter system used for a signal control circuit in an active noise cancellation apparatus, a signal control circuit in an active vibration control apparatus, an adaptive equivalent equipment in a communication apparatus, an echo canceler, a noise canceler, an adaptive line spectrum enhancer used in various digital signal processings.
2. Description of the Related Art
A Finite Impulse Response digital filter (hereinafter referred to as FIR digital filter) having a coefficient sequence which is variable and conveniently controlled is called an adaptive digital filter, and the adaptive digital filter is formed of an FIR digital filter portion and a coefficient control portion.
FIG. 10 is a diagram showing a representative construction of an adaptive digital filter. Referring to FIG. 10, the adaptive digital filter includes a unit delay element 18, a multiplier 19 having a coefficient sequence h(i) to form filter coefficients and an adder 20, and a coefficient control portion 21 controlling the coefficient sequence h(i).
When input into the adaptive digital filter, a signal u (n) is subjected to conversion based on the following equation (1) in the FIR digital filter and a signal y (n) is output. N represents the number of taps in the digital filter. ##EQU1##
The above coefficient sequence h(i) is updated by coefficient control portion 21, and the output signal y (n) changes appropriately to be a desired signal. There are various algorithms for coefficient control portion 21 to control the coefficients, and a typical one is an LMS (Least Mean Square) algorithm by which coefficients are controlled based on the following equation (2): EQU h(i,n+1)=h(i,n)+.alpha.u(n-i)e(n) (2)
, where e (n) represents an error, i.e. the difference d(n)-y(n) between a desired signal d (n) and the output signal y (n), and .alpha. represents a convergence coefficient. .alpha. usually takes a small positive value to prevent its divergence. According to the algorithm, the coefficient sequence h(i) continues to be updated until an error signal e (n) becomes 0, and a desired signal corresponding to an input signal is consequently output from the adaptive digital filter.
FIG. 11 is an illustration of a construction of the above described adaptive digital filter applied to a signal processing portion in an active noise cancellation apparatus which suppresses noise by emitting from a speaker for noise silencing 5 a sound wave 180.degree. out of phase from and having the same amplitude as the noise from a noise source, thereby causing sound wave interference. The adaptive digital filter includes an FIR digital filter 6, a coefficient control portion 8, and a digital filter 7 for delay correction and gain correction of a signal from the output portion of FIR digital filter 6 to the input portion of coefficient control portion 8.
In the apparatus, a noise emitted from a noise source 1 is detected by a noise detecting microphone 3 and becomes an input signal u (n). The input signal u (n) is input into FIR digital filter 6, and subjected to a convolution operation based on the above equation (1) to be output as a noise silencing signal y (n), and when the noise silencing signal is output to speaker for noise silencing 5, sound wave interference is effected by y (n). Then, a result of the sound wave interference is detected at a noise silencing error detecting microphone 4, and the detected result is input as an error signal e.sub.0 for the noise silencing into coefficient control portion 8 which operates based on the LMS algorithm. Herein, -e.sub.0 corresponds to the difference d(n)-y(n) between a desired signal d (n) and the output signal y (n) in the above equation (2), and the coefficient sequence h(i) of FIR digital filter 6 is updated based on the following equation (3) similar to equation (2), so that an output from speaker for noise silencing 5 is adjusted to minimize the noise silencing error and the noise is canceled. EQU h(i,n+1)=h(i,n)-.alpha.u.sub.0 (n-i) e.sub.0 (n) (3)
In the equation, u.sub.0 (n) is a signal provided by addition of an amendment of a transfer characteristic from the output of FIR digital filter 6 to the output of noise silencing error detecting microphone 4 to the input signal u (n). Herein, h(i,n) represents a filter coefficient for a tap i at time n.
However, in the use of the above-described adaptive digital filter, when a signal having a frequency 1/3 or more as large as the sampling frequency fs of the adaptive digital filter is mixed into the input signal u (n) or the error signal e.sub.0 (n), a precision of noise silencing degrades due to phase errors in control, even increasing the noise in the frequency band, and sometimes howling results. More specifically, in active noise silencing, a noise is canceled by adding a sound of antiphase having the same amplitude as the noise, the effect of noise silencing is lost with 60.degree. phase error even if complete control of the amplitudes is achieved, and the noise is increased with a phase error more than that. Further, as the frequency of the noise is higher, the number of samples with respect to a waveform of one cycle decreases and the precision of the additional sound degrades, and control is liable to be unstable especially to a frequency 1/3 or more as large as the sampling frequency fs. More specifically, a noise of a high frequency propagating in a high order mode in a duct 2 mode cannot be silenced effectively.
The sampling frequency fs indicates the following: an input/output value of the digital filter is produced to time-discrete data u (n) as shown in equation (1). The u (n) is sampled by an A/D converting circuit 15 at intervals of time T. The sampling frequency fs of the digital filter is given by: EQU fs=1/T
Herein, the 0-order mode is a propagation mode in which a sound pressure is equalized (see FIG. 13(b)), when the sound pressure of a cross section A-B is inspected in a sound wave propagating a the duct (see FIG. 13(a)). The first order mode and the second order mode represent the cases with sound pressure waveforms as shown in FIGS. 13(c) and (d), respectively.
FIG. 14 is a representation showing the relation between the sound pressure waveform (a) of an actual noise and its sampled data (b). Referring to FIG. 14, when an actual signal is sampled at intervals of time T, values shown by dots are sampled as data. A waveform defined by a broken line is produced from the data shown by the dots, the amplitude and phase of the wave are both shifted from the original waveform, resulting in degradation in accuracy. Accordingly, howling is possibly encountered in the case of a frequency (1/2 sampling frequency) as shown in the figure.
The same problem will arise both in the case in which the transfer characteristic of digital filter 7 produced by previous measurement has a delay error, or in the case the characteristic itself has changed as speaker for noise silencing 5 or the like has changed with time.
With reference to FIG. 11, a description of the transfer characteristic of digital filter 7 is given. An output y of FIR digital filter 6 is transferred to speaker 5 via a D/A converting circuit 16 and an amplifier 13, and converted into a sound wave at speaker 5. Then, the sound wave is propagated in a duct 2, once again converted into an electrical signal at microphone 4, and input via an amplifier 14, and an A/D converting circuit 17 into a coefficient control portion (LMS circuit) 8 which controls filter coefficients. The term "transfer characteristic" herein means the relation between the output signal y of FIR digital filter 6 when noise source 1 does not emit sound and a signal appearing at the output of A/D converting circuit 17 through the above-stated path. The transfer characteristic is generally defined as a gain characteristic and a phase (delay) characteristic. Such transfer characteristic is provided to digital filter 7.
In other words, if the above-stated output signal y is input into digital filter 7, the characteristic of digital filter 7 is set so that the output of digital filter 7 is identical to the output of A/D converting circuit 17. The characteristic is decided based on data produced by previous measurement.
Assuming the filter coefficient of digital filter 7 is g(i) (where i=0.about.M-1: M is a filter tap number (the number of filter coefficients)), the data u.sub.0 (n) of digital filter 7 is given by the following equation: ##EQU2##
The filter coefficient g(i) defines the transfer characteristic of digital filter 7. The filter coefficient g(i) is produced by pervious measurement as described above.
Referring to FIG. 11, an error exists between the transfer characteristic of digital filter 7 which is produced by previous measurement and an actual transfer characteristic (D/A converting circuit 16.fwdarw.amplifier 13.fwdarw.speaker 5.fwdarw.duct 2.fwdarw.microphone 4.fwdarw.amplifier 14.fwdarw.A/D converting circuit 17), and the error causes an erroneous adjustment of the filter coefficient of FIR digital filter 6, resulting in howling. Among errors associated with transfer characteristics, the error in phase (delay) characteristic gives rise to a significant problem. When such a phase error is above 60.degree., the mean square value of e.sub.0 cannot be minimized by updating the filter coefficient based on equation (3), and, conversely, the value is increased.
More specifically, as shown in FIGS. 15(A) and 15(B), a sound having a waveform of antiphase as shown at (b) is supposed to be output. However, if a waveform (d) out of phase from this waveform (b) is output, the amplitude of a waveform produced by addition of two waves (c+d) is increased with the phase error of 60.degree. as a critical value. In other words, if a waveform having 60.degree. or more out of phase with respect to the antiphase is added (see FIG. 15(B)), the amplitude increases, and if a waveform having 60.degree. or more further out of phase from this is output for the purpose of adjusting this situation, the amplitude further increases, resulting in a howling phenomenon.
For the characteristic error of digital filter 7, the measurement error is considered to be primary. As for other causes, changes in the characteristics of speaker 5 and microphone 4 with time or change in the environment of duct 2, change in the speed of sound due to temperature changes, etc. cause differences between a previously measured transfer characteristic and an actual characteristic, sometimes resulting in howling. The effects brought about by such characteristic change is prominent for high frequency band. This is because if a delay uniformly changes by 100 .mu.s at all the frequencies (for example, due to change in the speed of sound by temperature change), the 100 .mu.s is translated into 18.degree. in terms of phase at 500 Hz, while it corresponds to 72.degree. at 2000 Hz. The situation may therefore be stable at 500 Hz, but at 2000 Hz there is a considerable possibility that howling takes place.
To cope with a high frequency signal, a method of increasing the sampling frequency fs is considered, but as the sampling frequency fs increases calculation cannot be finished within a sampling period, the timing of an output signal to an input signal is delayed, and effective control cannot be made. Connecting an analog filter for removing the high frequency component of a signal to a preceding stage to the input portion of the adaptive digital filter, but it takes a long period of time until the signal reaches the speaker since the delay time inherent to the analog filter is added to a signal processing period, and the size of the apparatus is increased in order to compensate for the time delay.
This problem due to the high frequency component mixing into the signal is also encountered when the adaptive digital filter is used for active vibration control. In vibration control, a controller is designed in a manner that the high order vibration modes of an object to be controlled is removed, but in that case, a phenomenon called spill over which causes oscillation in a removed higher order mode is sometimes effected. The cause for this spill over is the existence of a high order oscillation mode component mixed into a signal fed back to the controller. Similarly, when the above-described adaptive digital filter is used for the controller, precision degradation due to the high order mode component and instability in control are caused.